GaN/InGaN multi-quantum-wells (MQWs) micron light emitting diodes (µLEDs) with the size ranging from 10 to 300 µm are fabricated. Effects of strain relaxation on the performance of µLEDs have been investigated both experimentally and numerically. Kelvin probe force microscopy (KPFM) and micro-photoluminescence (µPL) are used to characterize the strained area on micron pillars. Strain relaxation and reducing polarization field in MQWs almost affects the whole mesa for 10 µm LEDs and about 4% area around the lateral for 300 µm LEDs. It makes a great contribution to high performance for smaller size µLEDs. Moreover, an indirect nanoscale strain measurement for µLEDs are provided.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Due to its high luminous efficiency and chromatic quality, GaN-based light emitting diode (LED) has a wide range of commercial applications in the field of solid-state lighting and full color displays. Comparing to conventional devices, micron LEDs (µLEDs) have faster pulse characteristics  and can work well under high injection level (tens of kA/cm2) [2–4]. Recently, more and more attention has been paid to their applications in visible light communication (VLC) [5–7]. The response frequency of devices, relating to the current injection level, determines data transmission rates in VLC system. 3dB bandwidth has been achieved as 800 MHz for a GaN-based µLED with the size of 24 µm .
High performances under the injection level of kA/cm2 for µLEDs are attributed to strain relaxation [8–10], as well as uniform current spreading, low junction temperature and little band-gap renormalization (BGR) effect [3,4,11,12]. In the early work, strain relaxation seems not significant for µLEDs because conventional Raman and PL measurements cannot measure the strain changes in the thin InGaN QWs or at the edge of the mesa [2, 13]. With the cathodoluminescence (CL) hyperspectral imaging and numerical modeling, the strain relaxation in micro-pillars has been demonstrated . However, CL measurement is destructive due to high-energy electron beam bombarding. Its resolution is also influenced by electron diffusion in the semiconductor materials.
Kelvin probe force microscopy (KPFM), a nondestructive method of detection, is widely applied to analyze nanostructures [15,16]. It is sensitive to the band bending of semiconductors and is used to study the role of polarity . In this work, KPFM was used to study the polarization field in partially strain relaxed InGaN/GaN MQWs of µLEDs with a spatial resolution of nanometer. Meanwhile, micro area photoluminescence (µPL) spectra of these samples were measured. µPL is also nondestructive but its resolution is limited by the size of laser spots. Using FDTD software and the APSYS package of Crosslight software, simulation was carried out to quantitatively analyze the results of KPFM and µPL measurements.
The epitaxial structure of the InGaN/GaN MQWs LED was grown by metal organic chemical vapour deposition (MOCVD). It consists of undoped GaN, Si-doped n-GaN, five periods of GaN/In0.2Ga0.8N MQW layers, Mg-doped Al0.07Ga0.93N electron-blocking layer (EBL) and Mg-doped p-GaN. Doping concentrations of n-GaN and p-GaN were 5 × 1018 cm−3 and 8 × 1017 cm−3 respectively. Conventional photolithography and inductively coupled plasma (ICP) etching technology were used to obtain micron pillars with the size ranging from 300 to 10 μm. KOH solution was applied to repair etching damages on the sidewall of our samples.
KPFM is installed on the Dimension ICON-PTAFM system of Bruker Co. It reflects the difference of work functions between tip and sample by measuring their contact potential difference (CPD). KPFM is sensitive to band bending and is suitable to study polarization field in μLEDs. The detailed principle is given elsewhere . In this work, a standard gold sample (ϕ = 5.1eV) was used to incriminate the tip’s work function. The results would be used in our simulation. AM-KPFM was chosen in our experiments. The interleave mode was set as lift and the lift scan height is 50 nm. We used Pt/Ir coated silicon tip whose resonance frequency and force constant is 75 kHz and 2.8 N/m respectively. Unlike metal samples, the effect of space-charge-layer (SCL) on the surface of semiconductor should be considered when KPFM was applied on our samples. µPL spectra were measured Via Raman Microscope of Renishaw Co. at room temperature. The spatial resolution of confocal PL spectroscope is about 2 microns. The mechanical precision is about 0.1 μm. Although the spatial resolution is lower than KPFM, µPL can characterize the optical properties in micro area. The integrated intensity and peak wavelength, which are also affected by strain relaxation, can be used as complementary for KPFM measurement.
The APSYS package of Crosslight software  was used to quantize energy band bending of our samples under equilibrium state, as well as the detailed recombination process of µLEDs under optical excitations. We also used FDTD software to simulate the light extraction efficiency (LEE) of our samples. These simulations helped to explore fundamentals behind the data obtained from KPFM and µPL. The parameters of different materials used in our calculation were the literature values getting from Joachim Piprek [20,21]. The band-structure parameters were followed to the work of Vurgaftman et al . Polarization charges would be automatically generated by the software when the values of screening factor were set in the different regions of the µLEDs according to the results measured by Zhang et al . The structure of sample we used in our simulation was the same as experimental one which is described above.
3. Results and discussion
Figure 1 shows the topographic image and CPD distribution on µLEDs with the diameter of 10 and 40 μm. In topographic image, the bright circle in the central area is p-GaN mesa and the dark surrounding is n-GaN. The height of the p-type mesa is about 550 nm for both 10 and 40 μm LEDs. Their sidewalls are sharp from p- to n-side. Surfaces are smooth for both p-type mesa and n-GaN bottom. The edge of the mesa is rougher for 10 μm LED than that for 40 μm LED. It may be due to the resolution of processing, such as photolithography, ICP etching, and so on. As to the CPD distribution, there is a dim mesa with a blurred boundary. The mesa is clearer for 40 μm LED than that for 10 μm LED. The CPD averages are about 540 mV for n-GaN bottoms of the two LEDs, while 775 and 850 mV for p-GaN mesas of 10 and 40 μm LEDs, respectively. The CPD slope is slower than the geometric slope at the sidewall of the mesa. The slope is much slower for 10 μm LED than that for 40 μm LED. Moreover, the CPD for 10 μm LED keep increasing from the edge to the center, and the mesa hunches up without a flat area. The CPD variation on the sidewall and mesa indicates the work function changing on the semiconductor, where the effects of doping and polarization should be considered.
The results of KPFM can be deduced by the following formula:
As mentioned before, SCL in semiconductor is an important component of the surface band bending in our experiments. The position of Fermi level at the surface is determined by doping concentration. When our sample contacts with the tip, band bending occurs, which have a great influence on work function. As shown in Fig. 2, upward band bending is induced by positive charges at the surface of n-GaN. Contrarily the band bending is downward for p-type GaN. APSYS is used to simulate the condition of band bending. For calculation, a new material named “tip” with the work function of 5.42 eV is defined. The default setting of GaN in the software (χ = 4.07 eV, Eg = 3.42 eV) is used. 0.82 eV upward band bending and 1.51 eV downward one are obtained for n-GaN and p-GaN respectively. The Fermi level is very close to the bottom of conductive band and their difference can be ignored for n = 5 × 1018 cm−3. However, there is about 0.2 eV between the Fermi level of p-GaN and the top of its valence band. According to the Eqs. (1) and (2), the CPD for n-type GaN is calculated as 530 mV, which is consistent with the experimental results.
The CPD of mesa affected by polarization field in InGaN/GaN MQWs is more complicated than that for n-GaN. Assisted by APSYS simulation, the effect of polarization in MQWs on the band structure is estimated. A “self-consistent” model, which removes the restriction of flat-band and couples the potential with charge density in a self-consistent manner, is used throughout our simulation. The device is under thermal equilibrium in the process of measuring. So there is no external bias in our simulation. The voltage and current on electrodes and any external light source or e-beam pump are all set zero. For conventional pn junction devices, the band will slope upward from n-type to p-type under the condition of equilibrium. However, the polarization charges in MQWs caused by lattice and thermal mismatch can change the band structure of devices, even slope becomes downward from n-type to p-type . Considering the compensation of fixed defects and other interface charges, there is about 50% discrepancy between the theoretical and experimental polarization induced charge . So the screen factor is chosen as 0.5 for full strained MQWs during the calculation. It is clear in Fig. 3 that the introduction of polarization can reduce the slope of the band, resulting in about 1.21 eV decrease in the difference between the bottom of conduction band and Fermi level. According to the simulation results, the CPD of the mesa is about 850 mV and the difference in CPD between the mesa and the n-GaN is about 300 mV, which well agrees with the KPFM measurements for the central area of 40 μm LED. As to the CPD variations on the sidewall and the mesa for 10 μm LED, the screen factor can be chosen as less than 0.5 for the strain relaxation in these area . As to the CPD of 775 mV for the central area of the mesa for 10 μm LED, the screen factor is correspondent to 0.47. It may be due to the global strain relaxation for 10 μm LED pillar .
Some researches show that the spontaneous polarization of GaN material can cause large band bending on the surface [26,27]. The band bending is often reduced by structure defects, Ga termination, oxidation of the surface and many other factors. The observed band bending difference of Ga- and N-polar surfaces are uncertain now. In this work, the tip condition, the structure (except the size) of the μLEDs, the Ga-polarity of GaN material are almost fixed, which will not influence the results of KPFM. On the smooth mesa, the small fluctuation of CPD shown in Fig. 1 may be attributed to the difference of spontaneous polarization on the surface.
The KPFM results measured on different size μLEDs are shown in Fig. 4. The relative position is defined as the ratio of the distance between the center and test point to the radius of μLED pillar. In Fig. 4, the CPD on the mesa keeps almost constant in the center area and shows an obvious slope at the edge. As mentioned above, the slow slopes are attributed to the reduction of polarization field caused by strain relaxation in InGaN/GaN MQWs. These results are more precise and less fluctuation than those in our previous CL work . According to the data of KPFM, the strain relaxation affected area ratios are obtained for LEDs with the different diameters, as listed in Table 1. The data of μPL are also listed in Table 1, which will be discussed later. The affected area ratios are much larger than those in CL results . The ratio is 37.5% for 40 μm LED, while the same ratio is for 10 μm LED in CL results. In Table 1, the ratio for 10 μm LED is 100%. Xie et.al mention that the blue shift which is less than 2 μm on average is hardly resolvable against the background fluctuation in CL maps , while it is well observed in KPFM images. It indicates smaller size μLEDs have large area ratio for strain relaxation. The partial strain relaxation occurs almost on the whole mesa for 10 μm LEDs. The strong strain induced polarization field separates the wave functions of electrons and holes. Therefore, μLEDs with smaller diameter are possible to have more excellent performance .
The effect of strain relaxation at the edge of μLEDs on the emission performance can be characterized by μPL measurement. Figure 5 shows μPL results for 40 μm LED. It is clear that PL intensities near the sidewall increase firstly and then go down. Correspondingly, there is blue shift followed by obvious red shift around the edge of pillar. The typical spectra recorded from edge and center areas are given in Fig. 5(c). Comparing to the spectrum measured in the center of mesa, there are about 1.26 times enhancement in integral intensity and 4 nm blueshift at the edge of the mesa. The blueshift and light emission enhancement can be attributed to strain relaxation, which will be demonstrated in the following APSYS simulation. Although the mechanical step of μPL measurement is accurate as 0.1 μm, test system’s resolution is limited by the size of laser spot (about 2 μm). When the measured spot is very close to the sidewall, laser excited both the quantum wells and the exposure n-GaN bottom. The broad yellow band is around 550 nm for n-GaN layer. Its PL intensity is much less than the quantum wells. It leads to the reduction in PL intensity and redshift when the laser spot moves across the sidewall of μLED mesa.
According to above experimental results, the 40μm LED mesa can be divided to fully strained area and partially strain relaxation area, which are located at center and edge areas, respectively. So the PL measurements in the two areas are simulated by APSYS. An incident light is defined as the He-Cd laser with the wavelength of 325 nm, whose power density is same as 3.29 × 107 W/m2. The effective light power is required to be ramped up to the defined value controlled by the program in APSYS. The screen factor for polarization charge is set as 0.5 for full strained InGaN QWs according to the experimental [25, 29]. The strain is partially relaxed at the edge of μLED pillars. For 40 μm LED, Fig. 1(a) shows about 100mV difference between the center and the edge of the mesa. So the screen factor is calculated as 0.38 at the edge area according to the results of KPFM.
Figure 6 shows the simulated PL results for two different areas on the mesa of 40 μm LED. The spontaneous emission rate corresponds to the PL intensity. The PL peak intensity enhances about 1.18 times and the emission peak blue shifts 5 nm for the strain relaxation area compared with the ref one. The output from the APSYS shows that the hole concentration decreases gradually from p-GaN to n-GaN, while electron one keeps constant. The light is almost emitted from the nearest QW closing to p-GaN. So the energy band diagram and wave function distribution of the fifth quantum well are extracted, as shown in Fig. 6(b). Strain relaxation results in the change of band bending reduction in MQWs. The band gaps of InGaN QWs are 2.676 and 2.706 eV for the center and edge area of the mesa respectively. Correspondingly the peak wavelengths for different areas are 464 and 459 nm. Meanwhile, the difference between the peak of electron and hole wave function reduces 0.52 nm for strain relaxation area. In other words, the overlap of electron and hole wave function increases in these strain relaxation areas, which explain PL intensity enhancement shown in Fig. 6(a).
The above simulation made by APSYS shows the effect of strain relaxation on internal quantum efficiency (IQE) which influence light output characteristics. Light extraction efficiency (LEE) is another important factor that affect the results of PL and was analyzed with the help of FDTD software. According to some reports , a dipole can represent electron-hole recombination. So it was chosen as the light source and was placed at the middle of MQWs (290 nm below the top GaN surface). By moving the position of the dipole along radial direction, position dependent LEE can be calculated by FDTD. The wavelength of light source was set to 460 nm. The refraction index of GaN is 2.5 according to the report of Sun et.al . The LEE was 36.7% and 41.3% when the light source was set at the center and around the edge of mesa respectively. Combining with the results of APSYS and FDTD, the enhancements in PL peak intensity and PL integral intensity are 1.32 times and 1.27 times respectively. The results of simulation is very close to our experimental results (shown in Fig. 5(c)).
Figure 7 shows dependencies of PL integral intensity and peak wavelength on relative position of the mesa of μLEDs with different diameter. The curves are separated by moving upward several units along the ordinate. In Fig. 7(a), it is shown that the PL intensities near the sidewall rise firstly and then go down for 300, 160, 80 and 40 μm LEDs. The rising and falling edges become slower when the sizes of the μLEDs become smaller. For 10 μm LED, the rising and falling edges spread in the most area of the mesa. In Fig. 7(b), there is a blue shift of several nanometers near the edge in each curve. For large size μLEDs, the blue shift area is relatively little. According to the above analysis, the blue shift is due to the strain relaxation at the edge of the mesa. For 10 μm LED, blue shift appears on the whole mesa. It is attributed to the global strain relaxation , which is also evidenced by KPFM experiment. The ratios of strain relaxation affected area measured by µPL are listed in Table 1. Taking the large laser spot into consideration, the results of µPL are consistent with that of KPFM. From the data in Table 1 and the similar curves in the Figs. 5 and 7(a), the µPL measurements demonstrate the KPFM results, while KPFM provides a high spatial resolution of nm.
As to the strain induced polarization field, it can reduce the overlapping of wave functions between electrons and holes, cause current leakage in InGaN/GaN MQWs and so on [13, 28, 32–34]. The previous simulations [2-3] show that the current crowding is more serious around the sidewall. Polarization field becomes more detrimental due to the carrier confinement and BGR effect [2, 29]. For smaller size μLEDs, global and edge area strain relaxation will alleviate the effects of the polarization field, which can enhance the luminous efficiency under high injection level. The strain characterization under nm scale is very significant for design and fabrication of small size μLEDs. The KPFM is one of the important methods to do this work.
In summary, KPFM and µPL measurements were carried out to characterize the strain relaxation on the mesa of µLEDs. µPL also showed the light output distribution of µLEDs. The effect of strain induced polarization in MQWs on the band structure of µLEDs was analyzed under equilibrium state and light excitation using APSYS software. With the size of µLEDs decrease, the proportion of stain relaxation area tends to increase. The strong polarization field means the degradation of LEDs’ performance. KPFM is proved to be an effective method to measure the strain relaxation with nanometer spatial resolution.
Ministry of Science and Technology (2016YFB0400100); National Natural Science Foundation of China (61334009, 61674005); Guangdong Science and Technology Department (2016B010111001, 2014B090905002); Beijing Council of Science and Technology (Z161100001616010).
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